Finite Group Databasebeta

← #33004309

Subgroups — #33004309

Order 18688.

472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614916C211yesmaximal, characteristic
2C2×#17988385C214yesmaximal
3C4×#14556510C211yesmaximal, characteristic
4C73×#1801C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6C2×#14556589C2212yes—
7C2×#14556510C2212yes—
8C4×#11924012—21no—
9#17988517—21no—
10#17988517—21no—
11#17988492C412yes—
12#17988485—21no—
13#17988485—21no—
14C4×C4⋊Dic73C411yescharacteristic
15#17988385—28no—
16#17988356—21no—
17C2×C4×Q8×C73C2211yescharacteristic
18#423×C73—21no—
19C2×#101×C73C2212yes—
20#343×C73—21no—
21C22×Dic146C2×C412yes—
22C2×#11924012—22no—
23#14556591—41no—
24#14556591—41no—
25#14556589—24no—
26#14556589—24no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×#11924007—22no—
31C2×#11924007—22no—
32C2×C4×Dic73C2×C412yes—
33#14556510—22no—
34#14556510D414yes—
35#14556502—41no—
36C4×#10596831—41no—
37#14556498—21no—
38#14556498—22no—
39#14556498—22no—
40C22×Q8×C73C2311yescharacteristic
41C2×M16×C73—22no—
42C4×Q8×C73—41no—
43C4×Q8×C73—41no—
44C2×C4⋊C4×C73C2×C411yescharacteristic
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C42×C73C2×C411yescharacteristic
48C2×C42×C73D411yescharacteristic
49C2×C42×C73D411yescharacteristic
50C4⋊C8×C73—41no—
51C4⋊C8×C73—41no—
52#101×C73—24no—
53C2×Dic146—24no—
54C2×Dic146—42no—
55C2×Dic146—42no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58#11924012—24no—
59#11924012—42no—
60C2×#10596831—42no—
61C4⋊Dic73—24no—
62C4⋊Dic73—42no—
63C4⋊Dic73—41no—
64C4⋊Dic73—41no—
65#11924007—44no—
66#11924007—42no—
67#11924007—42no—
68C4×Dic73—24no—
69C2×Q8×C73—41no—
70C2×Q8×C73—41no—
71C2×Q8×C73C2×D412yes—
72C2×Q8×C73#4112yes—
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22×C411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79C22×C4×C73C2×D411yescharacteristic
80M16×C73—42no—
81M16×C73—42no—
82C2×C8×C73—42no—
83C4⋊C4×C73—41no—
84C4⋊C4×C73—41no—
85C4⋊C4×C73—41no—
86C42×C73—21no—
87C42×C73—21no—
88C42×C73—21no—
89C42×C73—21no—
90C42×C73—21no—
91C42×C73—21no—
92C23×C73C2×C22⋊C411yescharacteristic
93Q8×C73—42no—
94Q8×C73—42no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73#9911yescharacteristic
109C2×C4×C73#9911yescharacteristic
110C2×C4×C73C4×D412yes—
111C2×C4×C73#12112yes—
112C2×C4×C73#12411yescharacteristic
113C2×C4×C73#12711yescharacteristic
114C2×Dic73—24no—
115C2×Dic73—42no—
116C2×Dic73—42no—
117C2×Dic73—42no—
118C2×Dic73—42no—
119C2×Dic73—42no—
120Dic146—84no—
121C8×C73—82no—
122#10596831—44no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73#39011yescharacteristic
126C22×C73C2×#9911yescharacteristic
127C22×C73#41011yescharacteristic
128C4×C73—21no—
129C4×C73—22no—
130C4×C73—21no—
131C4×C73—22no—
132C4×C73—21no—
133C4×C73—41no—
134C4×C73—41no—
135C4×C73—41no—
136C4×C73#35612yescomplemented
137Dic73—44no—
138Dic73—82no—
139#13227—731nomaximal, Sylow
140C2×C73—21no—
141C2×C73—21no—
142C2×C73#196411yescharacteristic
143C2×C73C2×#35611yescharacteristic
144C2×C73#213511yescharacteristic
145#2546—731no—
146C2×#356—734no—
147#1801D7311yescharacteristic
148C4×#101—731no—
149C73#1322711yescharacteristic, complemented, Sylow
150C2×C4⋊Q8—732no—
151C2×C4⋊Q8—731no—
152C2×C4×Q8C2×D7311yescharacteristic
153#423—21no—
154C2×#101—732no—
155C2×#101C2×D7312yes—
156C4×M16—1461no—
157#398—1461no—
158#398—1461no—
159#391—732no—
160#389—1461no—
161#389—1461no—
162C4×C4⋊C4—731no—
163#356—1468no—
164#343—21no—
165#343—1461no—
166C22×Q8—732no—
167C22×Q8C22×D7311yescharacteristic
168C2×M16—22no—
169C2×M16—1462no—
170C4⋊Q8—2921no—
171C4⋊Q8—2921no—
172C4⋊Q8—1464no—
173C4⋊Q8—1464no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—1461no—
177C2×C4⋊C4—1461no—
178C2×C4⋊C4—1462no—
179C2×C4⋊C4—1462no—
180C2×C4⋊C4—1461no—
181C2×C4⋊C4C4×D7311yescharacteristic
182C2×C4⋊C4D29211yescharacteristic
183C2×C4⋊C4C22⋊D7311yescharacteristic
184C2×C42—732no—
185C2×C42C4×D7311yescharacteristic
186C2×C42D29211yescharacteristic
187C2×C42C22⋊D7311yescharacteristic
188C4⋊C8—41no—
189C4⋊C8—41no—
190#101—24no—
191#101—734no—
192#101—1462no—
193#97—2921no—
194C4×C8—2921no—
195#95—1461no—
196#95—1462no—
197#95—1462no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—2922no—
201C2×Q8—2922no—
202C2×Q8—1464no—
203C2×Q8D4×D7312yes—
204C2×Q8#1192402912yes—
205C22×C4—1462no—
206C22×C4—1462no—
207C22×C4#1192400511yescharacteristic
208C22×C4#1192400511yescharacteristic
209C22×C4#1192400511yescharacteristic
210C22×C4#1192400511yescharacteristic
211C22×C4C2×C4×D7311yescharacteristic
212C22×C4C2×C22⋊D7311yescharacteristic
213C22×C4C2×D29211yescharacteristic
214M16—42no—
215M16—42no—
216M16—2922no—
217M16—1464no—
218C2×C8—42no—
219C2×C8—2922no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—2922no—
224C4⋊C4—2921no—
225C4⋊C4—2921no—
226C4⋊C4—2924no—
227C4⋊C4—2922no—
228C4⋊C4—2922no—
229C4⋊C4—1464no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—1464no—
237C23C2×#1192400511yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—5844no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—2922no—
255C2×C4—2922no—
256C2×C4—2922no—
257C2×C4—2922no—
258C2×C4—2922no—
259C2×C4—1464no—
260C2×C4#1455650511yescharacteristic
261C2×C4#1455650511yescharacteristic
262C2×C4#1455655312yes—
263C2×C4#1455656612yes—
264C2×C4#1455658011yescharacteristic
265C2×C4#1455658711yescharacteristic
266C8—82no—
267C8—2924no—
268C22—21no—
269C22—21no—
270C22#1798848811yescharacteristic
271C22C2×#1455650511yescharacteristic
272C22#1798856011yescharacteristic
273C4—21no—
274C4—22no—
275C4—22no—
276C4—21no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—2924no—
282C4—5842no—
283C4#1798838512yescomplemented
284C2—21no—
285C2—21no—
286C2#2261076611yescharacteristic
287C2C2×#1798838511yescharacteristic
288C2#2261162511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC22×Q8C22×D73
FittingC73×#1801C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC22×Q8×C73C23
hypercenter#1801D73
hypocenterC73#13227
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
136. C4×C73#356semidirect
149. C73#13227semidirect
283. C4#17988385semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226149162
C2×#179883852
C4×#145565102
C73×#18012
#1322773